Update Mirroring Script to Include Verification of gh auth status

[mhlidd]

What Does This Do

Currently, a PR may exist but cannot be "found" because the user is not logged in to GH CLI. This PR updates the script to include a check to verify that the user is logged into GH CLI.

Motivation

Additional Notes

Contributor Checklist

• Format the title according the contribution guidelines
• Assign the type: and (comp: or inst:) labels in addition to any useful labels
• Don't use close, fix or any linking keywords when referencing an issue.
  Use solves instead, and assign the PR milestone to the issue
• Update the CODEOWNERS file on source file addition, move, or deletion
• Update the public documentation in case of new configuration flag or behavior

Jira ticket: [PROJ-IDENT]

[github-actions]

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[datadog-datadog-prod-us1]

🎯 Code Coverage
• Patch Coverage: 100.00%
• Total Coverage: 59.67% (-0.00%)

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[PerfectSlayer]

👏 praise: ‏Thanks for the improvement!